基于高精度时频瞬时相位谱的多尺度曲率及其应用
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摘要
基于地震信号瞬时相位估算的曲率属性具有较高的分辨率,被广泛应用于地震数据的不连续性检测。为进一步提高曲率属性的估算精度,提高地震数据对地质构造的刻画能力,基于时频分析方法具有多尺度分辨能力的特点,提出了基于改进的短时傅里叶变换获得高精度时频瞬时相位谱的多尺度曲率属性估算方法。改进的短时傅里叶变换对待分析实信号的解析信号加上对称时窗函数并进行傅里叶变换,从而获得高精度时频瞬时振幅谱、高精度时频初始相位谱和高精度时频瞬时相位谱。为减少随机噪声对高精度时频瞬时相位谱的影响,利用高精度时频瞬时振幅谱的峰值振幅及其对应的高精度时频瞬时相位谱重构输入信号,并对重构信号进行改进的短时傅里叶变换,获得稳定的高精度时频瞬时相位谱,在此基础上进行高精度多尺度曲率估算。利用合成数据及实际三维地震数据的应用结果验证了方法的有效性。
Curvature estimation based on the instantaneous phase of seismic signal has high precision and is widely used for discontinuity detection.To further improve the precision of curvature estimation and the ability of seismic data to describe geological structures,according to the multiscale resolution of time-frequency analysis,this paper proposes the modified short-time Fourier transform(STFT) to obtain high-precision time-frequency instantaneous phase spectrum for multiscale curvature estimation.The modified STFT applies a symmetric function windowed Fourier transform to the analytic signal of a real signal,in order to obtain the high-precision time-frequency instantaneous amplitude spectrum, high-precision time-frequency initial phase spectrum and high-precision time-frequency instantaneous phase spectrum.To minimize the effect of random noise on the high-precision time-frequency instantaneous phase spectrum,the input real signal is reconstructed by the peak high-precision time-frequency instantaneous amplitude spectrum and its corresponding high-precision time-frequency instantaneous phase spectrum;thereafter,the modified STFT is applied to the reconstructed real signal to obtain stable high-precision time-frequency instantaneous phase spectrum for high-precision multiscale curvature estimation.Tests conducted on both synthetic data and a real 3 D seismic data verified the effectiveness of the proposed method.
Curvature estimation based on the instantaneous phase of seismic signal has high precision and is widely used for discontinuity detection.To further improve the precision of curvature estimation and the ability of seismic data to describe geological structures,according to the multiscale resolution of time-frequency analysis,this paper proposes the modified short-time Fourier transform(STFT) to obtain high-precision time-frequency instantaneous phase spectrum for multiscale curvature estimation.The modified STFT applies a symmetric function windowed Fourier transform to the analytic signal of a real signal,in order to obtain the high-precision time-frequency instantaneous amplitude spectrum, high-precision time-frequency initial phase spectrum and high-precision time-frequency instantaneous phase spectrum.To minimize the effect of random noise on the high-precision time-frequency instantaneous phase spectrum,the input real signal is reconstructed by the peak high-precision time-frequency instantaneous amplitude spectrum and its corresponding high-precision time-frequency instantaneous phase spectrum;thereafter,the modified STFT is applied to the reconstructed real signal to obtain stable high-precision time-frequency instantaneous phase spectrum for high-precision multiscale curvature estimation.Tests conducted on both synthetic data and a real 3 D seismic data verified the effectiveness of the proposed method.
引文
[1] CHOPRA S,MARFURT K J.Seismic attributes:A historical perspective[J].Geophysics,2005,70(5):3-28
[2] MARFURT K J.Techniques and best practices in multiattribute display[J].Interpretation,2015,3(1):1-23
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[4] MARFURT K J.Robust estimates of 3D reflector dip and azimuth[J].Geophysics,2006,71(4):29-40
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[6] MARFURT K J,AI-DOSSARY S.3D volumetric multispectral estimates of reflector curvature and rotation[J].Geophysics,2006,71(5):41-51
[7] 李建雄,崔全章,魏小东.地震属性在微断层解释中的应用[J].石油地球物理勘探,2011,46(6):925-929 LI J X,CUI Q Z,WEI X D.Application of seismic attributes in micro-fault interpretation[J].Oil Geophysical Prospecting,2011,46(6):925-929
[8] 印兴耀,高京华,宗兆云.基于离心窗倾角扫描的曲率属性提取[J].地球物理学报,2014,57(10):3411-3421 YIN X Y,GAO J H,ZONG Z Y.Curvature attribute based on dip scan with eccentric window[J].Chinese Journal of Geophysics,2014,57(10):3411-3421
[9] 徐红霞,沈春光,李斌,等.多属性分析技术在碳酸盐岩断溶体预测中的应用[J].石油地球物理勘探,2017,52 (增刊2):158-163XU H X,SHEN C G,LI B,et al.Fault-karst carbonate reservoir prediction with comprehensive multi-attribute analysis[J].Oil Geophysical Prospecting,2017,52(S2):158-163
[10] BAHORICH M,FARMER S.3-D seismic discontinuity for faults and stratigraphic features:The coherence cube[J].The Leading Edge,1995,14(10):1053-1058
[11] GERSZTENKORN A,MARFURT K J.Eigenstructure-based coherence computations as an aid to 3-D structural and stratigraphic mapping[J].Geophysics,1999,64(5):1468-1479
[12] MARFURT K J,SUDHAKER V,GERSZTENKORN A.Coherency calculations in the presence of structural dip[J].Geophysics,1999,64(1):104-111
[13] WU X.Directional structure-tensor-based coherence to detect seismic faults and channels[J].Geophysics,2017,82(2):13-17
[14] PICOU C,Utzmann R.La “coupe sismique vectorielle”[J].Geophysical Prospecting,1962,10(4),497-516
[15] BARNES A E.Theory of 2-D complex seismic trace analysis[J].Geophysics,1996,61(1):264-272
[16] BARNES A E.A tutorial on complex seismic trace analysis[J].Geophysics,2007,72(6):33-43
[17] MARFURT K J,KIRLIN R L,FARMER S L,et al.3-D seismic attributes using a semblance-based coherency algorithm[J].Geophysics,1998,63(4):1150-1165
[18] BAKKER P,VAN VLIET L J,VERBEEK P W.Edge preserving orientation adaptive filtering[J].IEEE Computer Society Conference on Computer Vision and Pattern Recognition,1999,1(1):1535-1540
[19] LUO Y,WANG Y E,ALBINHASSAN N M,et al.Computation of dips and azimuths with weighted structural tensor approach[J].Geophysics,2006,71(1):119-121
[20] WANG X K,YANG C C,CHEN W C,et al.Estimating the dip by constructing gradient structure tensor on instantaneous phase[J] Expanded Abstracts of 84th Annual Internat SEG Mtg,2014:1580-1584
[21] WANG X K,CHEN W C,GAO J H,et al.Estimate dip by combining gradient structure tensor and multi-window[M].Expanded Abstracts of 85th Annual Internat SEG Mtg,2015:1722-1727
[22] GABOR D.Theory of communication[J].Journal of the Institute of Electrical Engineers,1946,93:429-457
[23] STOCKWELL R G,MANSINHA L,LOWE R P.Localization of the complex spectrum:The S-transform[J].IEEE Transactions on Signal Processing,1996,44(4):998-1001
[24] PINNEGAR C R,MANSINHA L.The S-transform with windows of arbitrary and varying shape[J].Geophysics,2003,68(1):381-385
[25] 高静怀.广义S变换与薄互层地震响应分析[J].地球物理学报,2003,46(4):526-532GAO J H.Generalized S transform and seismic response analysis of thin interbeds[J].Chinese Journal of Geophysics,2003,46(4):526-532
[26] 熊晓军,贺振华,黄德济,等.广义S变换在地震高分辨处理中的应用[J].勘探地球物理学进展,2006,29(6):415-418XIONG X J,HE Z H,HUANG D J,et al.Application of generalized S transform in seismic high resolution processing[J].Progress in Exploration Geophysics,2006,29(6):415-418
[27] 张固澜.基于改进的广义S变换的低频吸收衰减梯度检测[J].地球物理学报,2011,54(9):2407-2411 ZHANG G L.Low frequency absorption attenuation gradient detection based on improved generalized S transform[J].Chinese Journal of Geophysics,2011,54(9):2407-2411
[28] KRONLAND-MARTINET R,MORLET J,GROSSMANN A.Analysis of sound patterns through wavelet transforms[J].International Journal of Pattern Recognition and Artificial Intelligence,1987,1(2):273-302
[29] 高静怀,汪文秉,朱光.小波变换与信号瞬时特征分析[J].地球物理学报,1997,40(6):821-832GAO J H,WANG W B,ZHU G.Wavelet transform and instantaneous attributes analysis[J].Chinese Journal of Geophysics,1997,40(6):821-832
[30] CASTAGNA J P,SUN S J.Comparison of spectral decomposition methods[J].First Break,2006,24(3):75-79
[31] 陈文超,高静怀,包乾宗.基于连续小波变换的自适应面波压制方法[J].地球物理学报,2009,52(11):2854-2861CHEN W C,GAO J H,BAO Q Z.Adaptive attenuation of ground roll via continuous wavelet transform[J].Chinese Journal of Geophysics,2009,52(11):2854-2861
[32] 王晓凯,高静怀,陈文超,等.基于高维连续小波变换的地震资料不连续性检测方法研究[J].地球物理学报,2016,59(9):3394-3407 WANG X K,GAO J H,CHEN W C,et al.Detecting method of seismic discontinuities based on high dimensional continuous wavelet transform[J].Chinese Journal of Geophysics,2016,59(9):3394-3407
[33] 刘伟.高分辨率时频分析方法及其在储层预测中的应用研究[D].北京:中国石油大学(北京),2016LIU W.Research on high-resolution time-frequency approaches and applications in reservoir prediction[D].Beijing:China University of Petroleum,2016
[34] TANER M T,KOEHLER F,SHERIFF R E.Complex seismic trace analysis[J].Geophysics,1979,44(6):1041-1063
[35] MCFADDEN P D,COOK J G,FORSTER L M.Decomposition of gear vibration signals by the generalized S transform[J].Mechanical Systems and Signal Processing,1999,13(5):691-707
[36] FOMEL S.Local seismic attributes[J].Geophysics,2007,72(3):29-33
[37] LIU J L,MARFURT K J.Instantaneous spectral attributes to detect channels[J].Geophysics,2007,72(2):23-31
[38] PURVES S.Phase and the Hilbert transform[J].The Leading Edge,2014,33(10):1164-1166
[39] ZHANG G L.Time-phase amplitude spectra based on a modified short-time Fourier transform[J].Geophysical Prospecting,2018,66(1):34-46
[2] MARFURT K J.Techniques and best practices in multiattribute display[J].Interpretation,2015,3(1):1-23
[3] MARFURT K J,KIRLIN R L.3-D broad-band estimates of reflector dip and amplitude[J].Geophysics,2000,65(1):304-320
[4] MARFURT K J.Robust estimates of 3D reflector dip and azimuth[J].Geophysics,2006,71(4):29-40
[5] ROBERTS A.Curvature attributes and their application to 3D interpreted horizons[J].First Break,2001,19(2):85-100
[6] MARFURT K J,AI-DOSSARY S.3D volumetric multispectral estimates of reflector curvature and rotation[J].Geophysics,2006,71(5):41-51
[7] 李建雄,崔全章,魏小东.地震属性在微断层解释中的应用[J].石油地球物理勘探,2011,46(6):925-929 LI J X,CUI Q Z,WEI X D.Application of seismic attributes in micro-fault interpretation[J].Oil Geophysical Prospecting,2011,46(6):925-929
[8] 印兴耀,高京华,宗兆云.基于离心窗倾角扫描的曲率属性提取[J].地球物理学报,2014,57(10):3411-3421 YIN X Y,GAO J H,ZONG Z Y.Curvature attribute based on dip scan with eccentric window[J].Chinese Journal of Geophysics,2014,57(10):3411-3421
[9] 徐红霞,沈春光,李斌,等.多属性分析技术在碳酸盐岩断溶体预测中的应用[J].石油地球物理勘探,2017,52 (增刊2):158-163XU H X,SHEN C G,LI B,et al.Fault-karst carbonate reservoir prediction with comprehensive multi-attribute analysis[J].Oil Geophysical Prospecting,2017,52(S2):158-163
[10] BAHORICH M,FARMER S.3-D seismic discontinuity for faults and stratigraphic features:The coherence cube[J].The Leading Edge,1995,14(10):1053-1058
[11] GERSZTENKORN A,MARFURT K J.Eigenstructure-based coherence computations as an aid to 3-D structural and stratigraphic mapping[J].Geophysics,1999,64(5):1468-1479
[12] MARFURT K J,SUDHAKER V,GERSZTENKORN A.Coherency calculations in the presence of structural dip[J].Geophysics,1999,64(1):104-111
[13] WU X.Directional structure-tensor-based coherence to detect seismic faults and channels[J].Geophysics,2017,82(2):13-17
[14] PICOU C,Utzmann R.La “coupe sismique vectorielle”[J].Geophysical Prospecting,1962,10(4),497-516
[15] BARNES A E.Theory of 2-D complex seismic trace analysis[J].Geophysics,1996,61(1):264-272
[16] BARNES A E.A tutorial on complex seismic trace analysis[J].Geophysics,2007,72(6):33-43
[17] MARFURT K J,KIRLIN R L,FARMER S L,et al.3-D seismic attributes using a semblance-based coherency algorithm[J].Geophysics,1998,63(4):1150-1165
[18] BAKKER P,VAN VLIET L J,VERBEEK P W.Edge preserving orientation adaptive filtering[J].IEEE Computer Society Conference on Computer Vision and Pattern Recognition,1999,1(1):1535-1540
[19] LUO Y,WANG Y E,ALBINHASSAN N M,et al.Computation of dips and azimuths with weighted structural tensor approach[J].Geophysics,2006,71(1):119-121
[20] WANG X K,YANG C C,CHEN W C,et al.Estimating the dip by constructing gradient structure tensor on instantaneous phase[J] Expanded Abstracts of 84th Annual Internat SEG Mtg,2014:1580-1584
[21] WANG X K,CHEN W C,GAO J H,et al.Estimate dip by combining gradient structure tensor and multi-window[M].Expanded Abstracts of 85th Annual Internat SEG Mtg,2015:1722-1727
[22] GABOR D.Theory of communication[J].Journal of the Institute of Electrical Engineers,1946,93:429-457
[23] STOCKWELL R G,MANSINHA L,LOWE R P.Localization of the complex spectrum:The S-transform[J].IEEE Transactions on Signal Processing,1996,44(4):998-1001
[24] PINNEGAR C R,MANSINHA L.The S-transform with windows of arbitrary and varying shape[J].Geophysics,2003,68(1):381-385
[25] 高静怀.广义S变换与薄互层地震响应分析[J].地球物理学报,2003,46(4):526-532GAO J H.Generalized S transform and seismic response analysis of thin interbeds[J].Chinese Journal of Geophysics,2003,46(4):526-532
[26] 熊晓军,贺振华,黄德济,等.广义S变换在地震高分辨处理中的应用[J].勘探地球物理学进展,2006,29(6):415-418XIONG X J,HE Z H,HUANG D J,et al.Application of generalized S transform in seismic high resolution processing[J].Progress in Exploration Geophysics,2006,29(6):415-418
[27] 张固澜.基于改进的广义S变换的低频吸收衰减梯度检测[J].地球物理学报,2011,54(9):2407-2411 ZHANG G L.Low frequency absorption attenuation gradient detection based on improved generalized S transform[J].Chinese Journal of Geophysics,2011,54(9):2407-2411
[28] KRONLAND-MARTINET R,MORLET J,GROSSMANN A.Analysis of sound patterns through wavelet transforms[J].International Journal of Pattern Recognition and Artificial Intelligence,1987,1(2):273-302
[29] 高静怀,汪文秉,朱光.小波变换与信号瞬时特征分析[J].地球物理学报,1997,40(6):821-832GAO J H,WANG W B,ZHU G.Wavelet transform and instantaneous attributes analysis[J].Chinese Journal of Geophysics,1997,40(6):821-832
[30] CASTAGNA J P,SUN S J.Comparison of spectral decomposition methods[J].First Break,2006,24(3):75-79
[31] 陈文超,高静怀,包乾宗.基于连续小波变换的自适应面波压制方法[J].地球物理学报,2009,52(11):2854-2861CHEN W C,GAO J H,BAO Q Z.Adaptive attenuation of ground roll via continuous wavelet transform[J].Chinese Journal of Geophysics,2009,52(11):2854-2861
[32] 王晓凯,高静怀,陈文超,等.基于高维连续小波变换的地震资料不连续性检测方法研究[J].地球物理学报,2016,59(9):3394-3407 WANG X K,GAO J H,CHEN W C,et al.Detecting method of seismic discontinuities based on high dimensional continuous wavelet transform[J].Chinese Journal of Geophysics,2016,59(9):3394-3407
[33] 刘伟.高分辨率时频分析方法及其在储层预测中的应用研究[D].北京:中国石油大学(北京),2016LIU W.Research on high-resolution time-frequency approaches and applications in reservoir prediction[D].Beijing:China University of Petroleum,2016
[34] TANER M T,KOEHLER F,SHERIFF R E.Complex seismic trace analysis[J].Geophysics,1979,44(6):1041-1063
[35] MCFADDEN P D,COOK J G,FORSTER L M.Decomposition of gear vibration signals by the generalized S transform[J].Mechanical Systems and Signal Processing,1999,13(5):691-707
[36] FOMEL S.Local seismic attributes[J].Geophysics,2007,72(3):29-33
[37] LIU J L,MARFURT K J.Instantaneous spectral attributes to detect channels[J].Geophysics,2007,72(2):23-31
[38] PURVES S.Phase and the Hilbert transform[J].The Leading Edge,2014,33(10):1164-1166
[39] ZHANG G L.Time-phase amplitude spectra based on a modified short-time Fourier transform[J].Geophysical Prospecting,2018,66(1):34-46
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